Method and system of suppressing data corresponding to noise using a model of noise propagation along a sensor streamer

ABSTRACT

Suppressing data corresponding to noise using a model of noise propagation along a sensor streamer. At least some of the example embodiments are methods including: reading a data set containing noise and seismic signals recorded by geophones disposed in a sensor streamer when the sensor streamer was within a body of water; determining locations of noise sources along the sensor streamer when the sensor streamer was within the body of water; and suppressing data of the data set corresponding to noise sources along the sensor streamer.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application Ser.No. 62/212,782 filed Sep. 1, 2015 titled “Suppression of Velocity NoiseUsing a Noise Propagation Model for Cable Vibrations.” This applicationalso claims the benefit of U.S. Provisional Application Ser. No.62/212,688 filed Sep. 1, 2015 titled “Vibration Analysis to IdentifyCable Propagation Modes and Models.” Both provisional applications areincorporated by reference herein as if reproduced in full below.

BACKGROUND

In marine geophysical surveying, one or more sensor streamers are towedbehind a tow vessel, and the sensor streamers collect data (e.g.,seismic, electromagnetic) regarding underground formations. Sensorstreamers used for seismic surveys may contain sensors that aresensitive to particle motion caused by seismic signals propagating pastthe sensor streamers. The sensors sensitive to motion are also sensitiveto noise propagating along the sensor streamer in the form of transversevibrations, such as noise caused by water flow by and around barnaclesand other marine growth as the sensor streamers are towed through thewater. Other noise sources are also possible, such as depth controldevices and debris tangled with the sensor streamers.

Regardless of the precise nature of the noise sources, the noise createdby such noise sources interferes with collection of seismic data, suchas by masking seismic signals of interest. Moreover, while all noisepropagates along the sensor streamer to some degree, low frequency noiseis attenuated less by the sensor streamer and thus low frequency noisepropagates further along the streamer. Low frequency noise may thereforemask seismic signals of interest recorded by sensors located along thestreamer far from the noise source location.

BRIEF DESCRIPTION OF THE DRAWINGS

For a detailed description of exemplary embodiments, reference will nowbe made to the accompanying drawings in which:

FIG. 1 shows an overhead view of a marine geophysical survey inaccordance with at least some embodiments;

FIG. 2 shows a side elevation view of a marine geophysical survey inaccordance with at least some embodiments;

FIG. 3 shows a frequency-position plot in accordance with at least someembodiments;

FIG. 4 shows a frequency-wavenumber plot in accordance with at leastsome embodiments;

FIG. 5 shows a method in accordance with at least some embodiments;

FIG. 6 shows a perspective, partial cut-away view of a sensor streamerin accordance with at least some embodiments;

FIG. 7 shows a source of vibrations in accordance with at least someembodiments;

FIG. 8 shows a source of vibrations in accordance with at least someembodiments;

FIG. 9 shows a source of vibrations in accordance with at least someembodiments;

FIG. 10 shows a method in accordance with at least some embodiments;

FIG. 11 shows a method in accordance with at least some embodiments; and

FIG. 12 shows a computer system in accordance with at least someembodiments.

DEFINITIONS

Certain terms are used throughout the following description and claimsto refer to particular system components. As one skilled in the art willappreciate, different companies may refer to a component by differentnames. This document does not intend to distinguish between componentsthat differ in name but not function. In the following discussion and inthe claims, the terms “including” and “comprising” are used in anopen-ended fashion, and thus should be interpreted to mean “including,but not limited to . . . .” Also, the term “couple” or “couples” isintended to mean either an indirect or direct connection. Thus, if afirst device couples to a second device, that connection may be througha direct connection or through an indirect connection via other devicesand connections.

“Cable” shall mean a flexible, axial load carrying member that alsocomprises electrical conductors and/or optical conductors for carryingelectrical power and/or signals between components.

“Rope” shall mean a flexible, axial load carrying member that does notinclude electrical and/or optical conductors. Such a rope may be madefrom fiber, steel, other high strength material, chain, or combinationsof such materials.

“Line” shall mean either a rope or a cable.

“Geophone” shall mean any sensor sensitive to motion, such as velocitysensors, and acceleration sensors (i.e., accelerometers). A pressuresensor shall not be considered a sensor sensitive to motion.

“Signal cone” shall mean a subset of data within a larger data set,where the subset of data represents noise and/or signals havingpropagation speeds equal to or above the speed of sound in water. Thepropagation speeds may be actual or apparent (e.g., caused by aliasing).

“De-propagating,” in relation to determining locations of noise sources,shall mean using a mathematical inverse of a model of noise propagationand a data set to determine locations of noise sources.

“Seismic signals” shall mean energy corresponding to a shot andreflected from an underground formation.

“Shot” shall mean the creation and/or release of acoustic energy as partof a geophysical survey.

“Voice coil” shall mean a device that moves a plunger relative to asolenoid, the plunger at least partially disposed within magnetic fluxpaths created by the solenoid when energized. The term voice coilincludes audio speakers.

“Known vibrations” shall mean vibrations traveling along a sensorstreamer where the origin location is known in advance of creation ofthe vibrations. Other information regarding the known vibrations mayalso be known in advance, such as spectral content and amplitude.

DETAILED DESCRIPTION

The following discussion is directed to various embodiments of theinvention. Although one or more of these embodiments may be preferred,the embodiments disclosed should not be interpreted, or otherwise used,as limiting the scope of the disclosure or the claims. In addition, oneskilled in the art will understand that the following description hasbroad application, and the discussion of any embodiment is meant only tobe exemplary of that embodiment, and not intended to intimate that thescope of the disclosure or the claims, is limited to that embodiment.

Various embodiments are directed to reducing noise in a data set createdduring a marine geophysical survey utilizing geophones in the sensorstreamers. More particularly, various embodiments are directed todetermining locations of noise sources along a sensor streamer when thesensor streamer was within a body of water, and suppressing noise fromthe data set corresponding to noise not only at the locations of thenoise sources, but also noise propagated away from the locations of thenoise sources along the sensor streamer. In example embodiments, thesuppressing of the noise is based on a model of noise propagation alongthe sensor streamer. In yet still other example embodiments, the modelof noise propagation along the sensor streamer is created and/ormodified based on known vibrations injected onto the sensor streamer,such as by a controlled source of vibrations. The specification firstturns to an example marine geophysical survey to orient the reader.

FIG. 1 shows an overhead view of a marine geophysical survey system 100in accordance with at least some embodiments. In particular, FIG. 1shows a survey vessel 102 having onboard equipment 104, such asnavigation, energy source control, and data recording equipment. Surveyvessel 102 is configured to tow one or more sensor streamers 106A-Fthrough the water. While FIG. 1 illustratively shows six sensorstreamers 106, any number of sensor streamers 106 may be used.

The sensor streamers 106 are coupled to towing equipment that maintainsthe sensor streamers 106 at selected lateral positions with respect toeach other and with respect to the survey vessel 102. The towingequipment may comprise two paravane tow lines 108A and 108B each coupledto the survey vessel 102 by way of winches 110A and 1106, respectively.The winches enable changing the deployed length of each paravane towline 108. The second end of paravane tow line 108A is coupled to aparavane 112, and the second end of paravane tow line 108B is coupled toparavane 114. In each case, the tow lines 108A and 108B couple to theirrespective paravanes through respective sets of lines called a “bridle.”The paravanes 112 and 114 are each configured to provide a lateral forcecomponent to the various elements of the survey system when theparavanes are towed in the water. The combined lateral forces of theparavanes 112 and 114 separate the paravanes from each other until theparavanes put one or more spreader lines 120, coupled between theparavanes 112 and 114, into tension. The paravanes 112 and 114 eithercouple directly to the spreader lines 120 or as illustrated couple tothe spreader line by way of spur lines 122A and 122B.

The sensor streamers 106 are each coupled, at the ends nearest thesurvey vessel 102 (i.e., the proximal ends) to a respective lead-incable termination 124A-F. The lead-in cable terminations 124 are coupledto or are associated with the spreader lines 120 so as to control thelateral positions of the sensor streamers 106 with respect to each otherand with respect to the survey vessel 102. Electrical and/or opticalconnections between the appropriate components in the onboard equipment104 and the sensors (e.g., 116A, 116B) in the sensor streamers 106 maybe made using lead-in cables 126A-F. Much like the paravane tow lines108 associated with respective winches 110, each of the lead-in cables126 may be deployed by a respective winch or similar spooling devicesuch that the deployed length of each lead-in cable 126 can be changed.

Still referring to FIG. 1, in many cases the sensor streamers 106 willbe associated with a plurality of streamer positioning devices. Forexample, the sensor streamers 106A-F may be associated with streamerpositioning devices 150A-F, respectively, shown coupled on the proximalends of the sensor streamers. In many cases, the streamer positioningdevices 150A-F may provide only depth control, as the lateral spacing ofthe sensor streamers near the proximal ends may be adequately controlledby the spreader lines 120, and twisting (i.e., rotation about the longaxis of the sensor streamer) may not be an issue close to the lead-incable terminations 124A-F. Further, the sensor streamers 106A-F may beassociated with streamer positioning devices 152A-F, respectively, showncoupled further from the proximal ends, and in some cases near thedistal ends of the sensor streamers 106A-F. The streamer positioningdevices 152A-F may provide not only depth control, but also lateralpositional control and may assist in preventing twisting experienced bythe sensor streamers. The streamer positioning devices may be EBIRD®wings available from Kongsberg Maritime AS, Kongsberg, Norway. In somecases each sensor streamer 106 may be 1000 to 10000 meters in length,and may comprise 20 or more streamer positioning devices.

FIG. 2 shows a side elevation view of the marine geophysical surveysystem 100 in order to discuss surface ghost effects. In particular,FIG. 2 shows survey vessel 102 towing a sensor streamer 106 in a towdirection 200. In the view of FIG. 2, only one sensor streamer 106 isvisible. The survey vessel 102 in the example marine geophysical surveysystem 100 also tows a seismic source 202 (e.g., air gun(s) or marinevibrator(s)) which periodically and selectively releases seismic energy,some of which propagates toward the seafloor 204. The seismic source 202creates seismic waves defining propagating wave fronts, but so as not tounduly complicate the figure only a few example directions of travel ofthe wave fronts are shown by lines 206 (but still referred to as seismicwaves 206). Down-going seismic waves 206 may be reflected off theseafloor 204 (and/or subsurface structures below the seafloor) and thusmove in an upward direction as up-going seismic waves 208 whichintersect the sensor streamer 106 at various sensor 116 locations andthereby create seismic signals. These incident up-going seismic waves208 then continue upward past the sensor streamer 106 and are reflectedoff the surface 210 of the water as down-going “surface ghost” waves212. These “surface ghost” waves intersect the streamer again at varioussensor locations. For simplicity of illustration, only two paths aredepicted in FIG. 2, while an actual seismic source would define manypaths originated at the seismic source 202, reflected off the seafloorand subsurface structures, and reflected as surface ghost waves off thewaters' surface 210.

In various embodiments, the sensors 116 at each location include ahydrophone, which is a device that is sensitive to pressure changes.Thus, as the up-going seismic waves 208 interact with the sensorstreamer 106, the hydrophones measure pressure changes associated withthe up-going seismic waves 208. However, and as mentioned above, theup-going seismic waves 208 continue past the sensor streamer 106 to thesurface 210 and are reflected as surface ghost waves 212. The reflectionat the surface 210 results in a 180 degree phase change (or, equivalentstated, the reflection results in a sign reversal) such that as thesurface ghost waves 212 again interact with the sensor streamer 106cancelling other up-going seismic waves. Stated otherwise, the surfaceghost waves cause destructive interference with up-going seismic wavesat the hydrophones, resulting in spectral notches.

To address this issue, the sensors 116 may also include collocatedsensors that are sensitive to particle motion (e.g., velocity sensors(with single direction or multi-direction sensitivity), or accelerationsensors (with single direction or multi-direction sensitivity)). Theparticle motion sensors are also known as geophones. The specificationdiscusses the mathematical aspects of the separation in greater detailbelow. Suffice it to say that the addition of a collocated geophone witha hydrophone at each “sensor” 116 location provides better overall dataafter processing.

However, geophones are susceptible to noise in the form of transversemechanical vibrations propagating along the sensor streamer. Noisepropagation is a function of many variables. For example, propagationvelocity of transverse mechanical noise may be a function of tension inthe sensor streamer, such that locations along the sensor streamer wheretension is higher (e.g., at the proximal ends of the sensor streamers)have higher propagation velocity of transverse mechanical noise thanlocations where tension is lower (e.g., distal ends of the sensorstreamers). Moreover, lower frequency noise (e.g., below about 50 Hertz(Hz)) tends to propagate further along the sensor streamer than higherfrequency noise (e.g., above about 50 Hz). Equivalently stated in termsof attenuation, higher frequency noise is attenuated more per unitdistance than lower frequency noise.

Noise sources along a sensor streamer may take many forms. Considerfirst a perfectly clean (i.e., no marine growth) sensor streamerdeployed and towed through the water. The perfectly clean sensorstreamer may have many noise sources. For example, streamer positioningdevices 150 and 152 may introduce broadband noise onto the sensorstreamer. Further, debris (e.g., fishing line, trash) may tangle with asensor streamer, and the debris may induce vibrations onto the sensorstreamer as the sensor streamer is towed through the water. Moreover,most devices in marine environments, including sensor streamers, becomehost locations for marine growth (e.g., barnacles, mussels). Thebarnacles and mussels may have sufficient structure that, as the sensorstreamer is towed through the water, vortex shedding of water around thebarnacles and mussels causes vibratory motion that is picked up as noiseby the geophones. Other noise sources are also possible. Thespecification now turns to a more mathematical discussion of separatingthe up-going seismic waves as well as various embodiments foridentifying and algorithmically removing the noise of various noisesources such as those discussed above.

The following discussion assumes a single streamer (e.g., one sensorstreamer towed behind the survey vessel) where each “sensor” comprises acollocated geophone measuring vertical velocity response V_(z) (e.g., agimballed geophone) and a hydrophone measuring total pressure P, whereboth the geophone and hydrophone respond perfectly to velocity andpressure, respectively. Considering a single location then, the up-goingpressure field can be derived as follows:P _(up)(ω,k _(χ))=½[P(ω,k _(χ))−α(ω,k _(χ) ,ρ,c)V _(z)(ω,k _(χ))]  (1)where P_(up) is the de-ghosted up-going pressure field, ω is the angularfrequency, k_(χ) is the spatial wavenumber, P is the measured pressureresponse of the hydrophone, ρ is the density of the water, c is thepropagation velocity of sound in the water, and V_(z) is the measuredvertical velocity response of the geophone. In words, the P_(up) data isa combination of the pressure response P of the hydrophone less aportion of the sensed vertical component of the particle velocity.Likewise the down-going pressure field can be derived as follows:P _(down)(ω,k _(χ))=½[P(ω,k _(χ))+α(ω,k _(χ) ,ρ,c)V _(z)(ω,k _(χ))]  (2)where P_(down) is the down-going pressure field. Again in words, theP_(down) data is a combination of the pressure response P of thehydrophone plus a portion of the sensed vertical component of theparticle velocity. The α term in both equations is a scale factorexpressed as:

$\begin{matrix}{{\alpha\left( {\omega,k_{\chi},\rho,c} \right)} = {\frac{\omega\;\rho}{\sqrt{\left( \frac{\omega}{c} \right)^{2} - k_{\chi}^{2}}} = \frac{{\rho\; c}\;}{\cos\;(\theta)}}} & (3)\end{matrix}$where θ is the emergence angle. The P_(up) data (equation (1)) may bethe de-ghosted deliverable for marine geophysical surveys that have aseismic component.

Conceptually, the data recorded by each hydrophone and geophone haveboth signal and noise components. The presence of both signal and noisecan be expressed mathematically as follows:d _(P)(ω,kχ)=P(ω,kχ)+ε(ω,kχ)  (4)d _(V)(ω,k _(χ))=V _(z)(ω,k _(χ))+υ(ω,k _(χ))  (5)where d_(P) is the pressure data, and ε is the noise in the pressuredata (hereafter just “pressure noise”), d_(V) is the velocity data, andυ is the noise in the velocity data (hereafter just “velocity noise”).Plugging equation (4) into equation (1) and mathematical manipulationresults in an estimated P_(up) as follows:P _(up) ^(est)(ω,k _(χ))=P _(up)(ω,k _(χ))+½[ε(ω,k _(χ))−α(ω,k _(χ),ρ,c)υ(ω,k _(χ))]  (6)where P_(up) ^(est) is the estimated P_(up) data. In words, the P_(up)^(est) is the up-going pressure field plus a noise component involvingboth the pressure noise and velocity noise. By mathematical manipulationof equation (6) it follows that total noise in the up-going pressurefield is therefore:ξ₀(ω,k _(χ))≡P _(up) ^(est)(ω,k _(χ))−P _(up)(ω,k _(χ))  (7)ξ₀(ω,k _(χ))=1/2[ε(ω,k _(χ))−α(ω,k _(χ) ,ρ,c)υ(ω,k _(χ))]  (8)where ξ₀ is the total noise. Equation (8) shows that both the pressurenoise ε(ω, k_(χ)) and the velocity noise υ(ω, k_(χ)) contribute thetotal noise ξ₀ in the up-going pressure field.

At least some of the example embodiments are directed to suppressing thevelocity noise υ(ω, k_(χ)) in equation (8) above. More particularly,various embodiments are directed to determining locations of noisesources along a sensor streamer when the sensor streamer was within abody of water by de-propagating the noise using a model of noisepropagation along the sensor streamer, and suppressing datacorresponding to noise sources along the sensor streamer. Thede-propagation and suppressing may create a down-sampled data set.

Consider, for purposes of explanation, a data set containing thereceived data from geophones along a single streamer during a collectionperiod of a seismic survey (e.g., 14 seconds of time after a shot). Eachgeophone records data comprising seismic signals passing the sensorstreamer, as well as noise. The seismic signals of interest may spanseveral tens of Hertz or more. The noise too may span many tens ofHertz, but the upper end of the noise frequency may be higher than theupper end of the seismic signal frequency. Thus, a single geophone mayrecord a range of signals having a range of frequencies.

FIG. 3 shows a frequency-position plot of an example data set acquiredby geophones of a single streamer during a collection period. Thevertical axis shows frequency of received signals, and the horizontalaxis identifies geophones along the sensor streamer by inline position(e.g., the sensor at inline position 11 being closer to the surveyvessel than the sensor at position 151). Thus, each entry on thehorizontal axis refers to a single geophone along the sensor streamer.The intensity of the information within the plot shows the magnitude ofthe data represented at the frequency and position. The example plot ofFIG. 3 again represents data collected over a collection period (e.g.,14 seconds of collection), but time is not expressly represented in theplot.

The plot of FIG. 3 visually conveys much information about the state ofthe sensor streamer during data collection. For example, the sensorstreamer had several noise sources spaced about the sensor streamerduring data collection, the noise sources represented by downward“spikes” of broadband data. In the example data set, spike 300 isrepresentative of a streamer positioning device and the noise induced onthe sensor streamer by the streamer positioning device. The downwardspike 302 and the plurality of spikes to the left of spike 302 representa group of broadband noise sources spaced along the sensor streamerduring data collection. FIG. 3 also shows that low frequency noiseexperiences less attenuation per unit distance travelled than highfrequency noise. In particular, the higher frequency portions (e.g.,above 100 Hz, and including spikes 300 and 302) have smaller breadth inthe horizontal direction (showing that the higher frequency noise isattenuated faster and thus propagates shorter distances along the sensorstreamer). Oppositely, the lower frequency portions (e.g., below 100 Hz,and particularly below 50 Hz) tend to have larger breadth in thehorizontal direction (showing that the lower frequency noise is lessattenuated and thus propagates longer distances along the sensorstreamer).

FIG. 4 shows a frequency-wavenumber plot of the example data set shownin FIG. 3. That is, FIG. 4 shows the same data set as FIG. 3, but in adifferent domain. The vertical axis shows frequency of received signals(with zero at the top and frequency increasing downward), and thehorizontal axis is wavenumber. Wavenumber refers to spatial frequency ofa wave (in this case acoustic energy in the form of either seismic wavesor noise). Spatial frequency may be thought of as cycle speed of anacoustic wave. Thus a “slow” wave may complete relatively few fullcycles over a unit distance, while a “fast” wave completes many fullcycles over the unit distance. Note, however, that the “slow” and “fast”designations refer only to how many cycles of the wave fit within a unitdistance, and do not speak to propagation speed of the waves through thewater. In FIG. 4 the horizontal axis has a center zero. Wavenumbers tothe left of center represent positive wavenumbers (i.e., acoustic wavespropagating toward the distal end of the sensor streamer), andwavenumbers to the right of center represent negative wavenumbers (i.e.,acoustic waves propagating toward the proximal end of the sensorstreamer).

FIG. 4 likewise shows several features of the data in the underlyingdata set. For example, the features 400 and 402 show lower frequencynoise propagating along the sensor streamer toward the distal end andthe proximal end, respectively. The slope of the features shows therelative speed of propagation of the noise features 400 and 402 alongthe sensor streamer (between about 20 and 40 meters per second (m/s)).The example plot also shows additional noise features 404 and 406, butthese noise features represent aliasing of the noise features 400 and402, respectively, caused by the finite spacing between the geophonesalong the sensor streamer.

Still referring to FIG. 4, signals of interest in the data of a marinegeophysical survey with a seismic component are the seismic wavespropagating through the water after reflection from formations below thesea floor, and the speed of sound in water is about 1500 m/s. Thus, inmost cases the seismic signals in the data corresponding to seismicwaves returned from the formations below the seafloor will reside withina signal cone 408 in the frequency-wavenumber domain of FIG. 4. That is,the data that resides within the triangular signal cone 408, such asseismic data 410, represent received signals whose propagation speedswere that of the speed of sound in water and above. However, some of thenoise may also actually or appear to (e.g., aliasing) propagate atspeeds approaching or exceeding the speed of sound in water, and thussome of the seismic signals of interest may be masked by noise. In theexample data set shown in the frequency-wavenumber domain of FIG. 4, theportions of the noise features 400 and 402 near the center of the plotreside within the signal cone 408. Moreover, some of the alias noisefeatures 404 and 406 may appear to be in the signal cone 408.

Related-art processing techniques to reduce noise in the data setinvolve a technique known as “dip filtering.” Dip filtering is atechnique that retains data having a combination of propagation velocityand emergence angles considered to cover the useful signals (e.g., dataresiding within a signal cone representative of propagation velocity of1500 m/s or more and emergence angles below about 70 degrees), andsuppresses or discards the remaining data. Still referring to FIG. 4,conceptually dip filtering is the suppression of all the data thatresides outside the signal cone 408 (e.g., the data associated withfeatures 400, 402, 404, and 406).

Referring simultaneously to FIGS. 3 and 4, various embodiments aredirected to reducing noise in a data set by a technique that complementsthe dip filtering of the related art. That is, because the data withinthe signal cone 408 is band limited in the wavenumber domain, theinventor of the present specification has found it is possible toestimate and suppress noise (e.g., aliased noise) within the signal coneusing data from the full data set (e.g., from the frequency-wavenumberdomain such as FIG. 4). More precisely then, various embodimentsde-propagate noise within a data set using a model of noise propagationalong the sensor streamer. Conceptually, the de-propagation “collects”the noise data at the various locations of noise sources. From thede-propagated data, the locations of the noise sources along the sensorstreamer when the sensor streamer was within the body of water can bedetermined, along with an indication of the noise level of each noisesource. Stated otherwise, the model of noise propagation along thesensor streamer includes a model of noise source locations along thesensor streamer, and by de-propagation the model of noise sourcelocations is solved such that the locations of noises sources areidentified. Once the locations of noise sources along the sensorstreamer are identified in the de-propagated data, the example methodsuppresses data of the de-propagated data set corresponding to noisesources along the sensor streamer. Suppressing data associated withlocations of noise sources may be thought of as down-weighting (and inthe extreme case removing) the data associated with the spikes 300 and302 of FIG. 3 (as the data in the spikes, being relatively highfrequency, does not propagate far from the noise source) as well asdown-weighting noise that propagated away from the locations of thenoise sources (e.g., removing much of the high intensity signal below 50Hz of FIG. 3). Replacement data may be created, such as interpolatingthe data within the signal cone that may have been down-weighted as partof the suppression of data. The specification now turns to a moremathematical treatment of the noise identification and suppression.

A data set containing velocity data can be written in thefrequency-position domain as:d _(V)(ω,χ)=V _(z)(ω,χ)+υ(ω,χ)  (9)where the terms are as previously defined. In words, the data setcontaining velocity data is made up of combined vertical velocityresponse V_(z) and velocity noise υ. Consider now a finite data set ofvelocity data in the frequency-position domain, from a single sensorstreamer, organized as an M×N matrix. Thus, the data set containingvelocity data can be written in matrix notation as:D=V _(z) +N  (10)where D is the velocity data in matrix format, V_(z) is the verticalvelocity response in matrix format, N is the noise in matrix format.Each row m in the matrix D (where m=1, 2, . . . , M) is frequency, andeach column n in the matrix D (where n=1, 2, . . . , N) is a sensorposition along the sensor streamer. A single frequency slice in thematrix D at f=f_(m) can thus be represented as:d _(m) =v _(z,m)+υ_(m)  (11)where d_(m) is the data at frequency f_(m), v_(z,m) is the verticalvelocity response at frequency f_(m), and υ_(m) is the velocity noise atfrequency f_(m).

As previously mentioned, the signal within the signal cone isband-limited in the wavenumber domain and can be created orreconstructed by interpolation from a more sparsely sampledrepresentation. In matrix-vector notation, the ability to createreplacement data may be expressed as:v _(z,m) =Q _(m)ξ_(m)  (12)where v_(z,m) is the reconstructed vertical velocity response data atfrequency f_(m), Q_(m) is a N×K interpolation matrix, and ξ_(m) is themore sparsely sampled representation at frequency f_(m) in the form of aK×1 signal vector. Plugging equation (12) into equation (11) results in:d _(m) =Q _(m)ξ_(m)+υ_(m).  (13)In words, the data d_(m) can be considered to be reconstructed verticalvelocity response data plus velocity noise. There are many ways toapproach deriving the more sparsely sampled representation ξ_(m). Forexample, one may impose a linear solution such as:ξ_(m) ^(est) =w _(m) ^(∥) d _(m)  (14)where ξ_(m) ^(est) is the estimated more sparsely sampledrepresentation, w_(m) ^(∥) is a weight vector (where ( )^(∥) denotes aconjugate transpose for which the expected squared error is reduced orminimized). Another approach to deriving the more sparsely sampledrepresentation ξ_(m) is to adopt a maximum likelihood approach withGaussian noise. A third approach is to employ Bayesian method byassigning zero mean Gaussian distribution for the noise term, use a flatprior distribution for the more sparsely sampled representation ξ_(m),and adopt a symmetric error criterion (e.g., minimized absolute error,squared error, or maximum error). All three approaches yield the samemore sparsely sampled representation ξ_(m) ^(est) as follows:ξ_(m) ^(est)=(Q _(m) ^(∥) R _(m) ⁻¹ Q _(m))⁻¹ Q _(m) ^(∥) R _(m) ⁻¹ d_(m)  (15)where R_(m) is the covariance matrix for the velocity noise υ_(m) infrequency slice f_(m). The functions of the factors of equation (15) canbe conceptually separated as follows:R _(m) ⁻¹ d _(m)  (16)Equation (16) implements the de-propagation of noise along withsuppression (e.g., re-weighting) of data in the data set correspondingto locations of noise sources along the sensor streamer after the noisedata is “collected” at the locations of the noise sources. That is, thecovariance matrix R_(m) mathematically implements the model of noisepropagation along the sensor streamer. Continuing with the remainingportions of equation (15):Q _(m) ^(∥) R _(m) ⁻¹ d _(m)  (17)implements dip filtering of the modified data; and(Q _(m) ^(∥) R _(m) ⁻¹ Q _(m))⁻¹ Q _(m) ^(∥) R _(m) ⁻¹ d _(m)  (18)implements a re-normalization of the dip-filtered reduced data set toensure that the re-weighting of the portion of equation (16) does notintroduce scale errors.

A component in the implementation of the various embodiments is creationof a model of noise propagation with which to create the covariancematrix R_(m). The model of noise propagation in various embodiments maybe based on several elements. First, the model may assume a finitenumber of noise sources along the sensor streamer, where each noisesource has a specific temporal power density. In some cases, each noisesource may be considered to be a white noise source, while in othercases each noise source may be considered to have a specific (non-white)temporal power spectral density. Moreover, the sensor streamer isconceptually divided into a plurality segments, for example the segmentsdefined between noise source locations and sensor locations (e.g.,between geophones). Each segment has a propagation speed as a functionof noise frequency and attenuation as a function of noise frequency.From the model of noise propagation, the covariance matrix R_(m) can bedetermined.

More mathematically then, the noise at any location along the sensorstreamer can be considered to be from a superposition of noise sourcesas follows:

$\begin{matrix}{{\upsilon\left( {\omega,\chi} \right)} = {\sum\limits_{l = 1}^{L}{\upsilon_{l}\left( {\omega,\chi} \right)}}} & (19)\end{matrix}$where υ(ω, χ) is the velocity noise as a function of the angularfrequency ω and the position along the sensor streamer χ, υ_(l)(ω, χ) isnoise contribution from an individual noise source (as a function ofangular frequency ω and position along the sensor streamer l), and L isthe total number of noise sources. The noise contribution from anindividual noise source is determined by the excitation and propagationparameters as:

$\begin{matrix}{{\upsilon_{\iota}\left( {\omega,\chi} \right)} = {{q\left( {\omega,\chi_{l}} \right)}{\prod\limits_{i \in N_{l}}\;{e^{{- \gamma}\;{i{(\omega)}}\Delta\;\chi_{i}}e^{j\;\omega\frac{{\Delta\chi}_{i}}{c_{i}}}}}}} & (20)\end{matrix}$where again υ_(l)(ω, χ) is noise contribution from an individual noisesource, q(ω, χ_(l)) is the noise source, N_(l) is the set of segmentsbetween the sensor and noise source q(ω, χ) at position χ_(i), ΔX_(i) isthe length of segment i, γ_(i) (ω) is the frequency dependentattenuation of segment i, and c, is the propagation speed of segment i.Equation (20) may be equivalently written as:

$\begin{matrix}{{\upsilon_{\iota}\left( {\omega,\chi} \right)} = {{q\left( {\omega,\chi_{\iota}} \right)}{e^{{\Sigma{({{{- \gamma}\;{i{(\omega)}}} + {j\frac{\omega}{c_{i}}}})}}\Delta\;\chi_{i}}.}}} & (21)\end{matrix}$Assigning the exponential portion of equation (21) the variableS_(l)(χ), equation (21) can thus be summarized as:υ_(i)(ω,χ)=S _(l)(χ)q(ω,χ_(l)).  (22)

Equations (19) through (22) represent a single frequency at a singlelocation. In matrix terms, the velocity noise at a single frequencyf=f_(m) can be expressed as:υ_(m) =S _(m)(γ,c)q  (23)where υ_(m) is the velocity noise matrix at all positions at frequencyf=f_(m), S_(m) is a complex-valued propagation in the streamer asfunction of attenuation γ and speed of sound c, and again q is the noisesource vector. The covariance matrix R_(m) may thus be expressed as:R _(m) =S _(m) R _(q) S _(m) ^(∥)  (24)where R_(q) is a matrix containing indications of the strength of thenoise sources on its diagonal (e.g., as determined from thede-propagation), and indications of any correlation between the noisesources on the off-diagonal locations. In most cases the noise sourceswill be uncorrelated, and thus the R_(q) matrix will be a diagonalmatrix.

With that mathematical background, the specification turns to FIG. 5,which is a flow diagram showing a method in accordance with variousembodiments, some or all of which may be implemented by a processor of acomputer system. In particular, the method starts (500) and proceeds toreading a data set containing noise and seismic signals recorded bygeophones disposed in a sensor streamer when the sensor streamer waswithin a body of water (block 504). The reading of the data set by acomputer system may be somewhat contemporaneous with acquiring the databy way of a marine geophysical survey (e.g., by way of a computer systemon the survey vessel 102), or the reading may be many days, months,years after the marine geophysical survey is performed (e.g., by aland-based computer system in a data analysis center).

The next step in the example method of FIG. 5 is determining locationsof the noise sources along the sensor streamer by de-propagating noisewithin the data set using the data set and a model of noise propagationalong the sensor streamer, along with an indication of the noise levelof each noise source (block 508). In reference to the earlierdescription, the de-propagation may also result in a set of dataindicative of amplitude and spectral content at each of the assumednoise source locations. Noise source locations whose amplitude and/orspectral content exceeds predetermined threshold (e.g., spectral contentabove 100 Hz) thus indicate the locations of the noise sources along thesensor streamer when the sensor streamer was within the body of water.Oppositely, some assumed noise source locations in the model may haveamplitude and/or spectral content below a predetermined threshold, andas such the locations associated with the other assumed noise sourcesare not indicative of noise source locations when the sensor streamerwas within the body of water.

Still referring to FIG. 5, the next step in the example method maycomprise suppressing data of the data set corresponding to noise sourcesalong the sensor streamer (block 512). Thereafter, the method maycomprise recording corrected data on a tangible data storage medium(block 516). In some cases, and again as discussed more mathematicallyabove, the method may include suppressing data that falls outside thesignal cone. Thereafter the method ends (block 520). It is noted thatthe replacement data, being originally based on data recorded bygeophones, is thus substantially free of noise caused by noisepropagation along the sensor streamer. The replacement data may then beused in further processing, such as calculating the deliverable data inthe form of P_(up) data (compensated for surface ghost waves).

In the various embodiments discussed to this point the model of noisepropagation (from which the covariance matrix R_(m) is constructed) maybe based on a set of assumptions about: locations of noise sources alongthe sensor streamer; noise propagation along the sensor streamer basedon parameters such as tension; noise propagation as a function offrequency; attenuation of noise along the sensor streamer as a functionof frequency; and perhaps even analytical tests on the particular sensorstreamer or related sensor streamers. In other embodiments, however, themodel of noise propagation in the sensor streamer may be created and/ormodified by inducing known vibrations on the sensor streamer while thesensor streamer is towed through the body of water. The data read bygeophones of the sensor streamer based on the known vibrations can thenbe used to create and/or update the model of noise propagation used toremove noise from the data set (which results in a down-sampled data),and from the down-sampled data set the replacement data set may becreated as discussed above. The specification now turns to an examplesensor streamer to discuss example mechanisms for insertion of the knownvibrations (e.g., vibrations above 100 Hz) onto the sensor streamer.

FIG. 6 shows a perspective, partial cut-away view of a sensor streamer106 in accordance with example embodiments. In particular, the sensorstreamer 106 comprises an outer jacket 600 of flexible and water proofmaterial. The outer jacket 600 thus defines an interior volume 602,which may be filled with a buoyant material (e.g., a gel with specificgravity less than water, or kerosene). Within the outer jacket 600resides a plurality of lines (e.g., ropes) that act as strength members,and in the example of FIG. 6 two such ropes 604 and 606 are present. Inoperation, the towing force that moves the sensor streamer 106 throughthe water is carried by the ropes 604 and 606. Though not specificallyshown, sensor streamer 106 may be made of a plurality of sectionsterminated on each end by metallic couplers. The ropes 602 and 604 aremechanically coupled to the metallic couplers on each end. Towing forceis transferred from one sensor streamer section to the next (i.e.,transferred from the ropes of one sensor streamer section to the nextsensor streamer section) by way of the metallic couplers.

The sensor streamer 106 also comprises a plurality of sensors at spacedlocations along the sensor streamer. In some cases, the sensors may beplaced at 0.5 meter intervals, but closer and more distance spacing isalso contemplated. In the example of FIG. 6 one such sensor 116 isshown, the sensor 116 residing at least in part within a sensor holder608. As discussed above, the sensor 116 is a collocated hydrophone andgeophone, but the hydrophone and geophone are not separately shown so asnot to unduly complicate the figure. Also within the outer jacket 600resides a communication pathway 610 which communicatively couples to thesensor 116 and other sensors along the sensor streamer 106. In somecases, the communication pathway 610 is set of metallic conductors(e.g., one or more pairs of twisted-pair cables), and in other cases thecommunication pathway 610 may be one or more optical fibers. In yetstill other cases, the communication pathway 610 may be a combination ofmetallic conductors (e.g., carrying power to various devices) andoptical fibers (e.g., carrying communication signals).

Still referring to FIG. 6, the example sensor streamer 106 furthercomprises a source of vibrations disposed at a predetermined locationalong the sensor streamer 106. The source of vibrations induces theknown vibrations on the sensor streamer at the predetermined locationwhile the sensor streamer is towed through water. One example source ofvibrations is shown in FIG. 6 as source of vibrations 612 disposed at apredetermined location with respect to and within outer jacket 600. Theexample source of vibrations 612 is communicatively coupled to thecommunication pathway 610, and the example source of vibrations 612selectively induces known vibrations onto the sensor streamer 106 basedon commands received through the communication pathway 610. The examplesource of vibrations 612 is shown to be mechanically coupled to theropes 604 and 606, and also mechanically coupled to the outer jacket600, such that the known vibrations are induced in both the ropes andthe outer jacket; however, in other cases the mechanical coupling to theouter jacket 600 may be omitted so that the known vibrations are inducedonly or predominantly in the ropes 604 and 606, and in yet still othercases the mechanical coupling to the ropes 604 and 606 may be omitted sothat the known vibrations are induced only or predominantly in the outerjacket 600. Specific examples of the structure of the source ofvibrations 612 are discussed more below.

The example source of vibrations 612 may be designed and constructed toinduce the known vibrations having an orientation perpendicular to aplane defined by the two ropes 604 and 606 at the location of the sourceof vibrations 612 (e.g., in the Z direction of the coordinate systemshown). Twisting of the sensor streamer 106 is possible, and thus theplane may be defined by the ropes 604 and 606 over a short distancebefore and after the location of the source of vibrations 612 (e.g., a10 centimeter section with the source of vibrations disposed in themiddle thereof). In other cases, the source of vibrations 612 may bedesigned and constructed to induce the known vibrations having anorientation parallel to the ropes at the location of the source ofvibrations 612 (e.g., in the X-Y plane of the coordinate system shown).Again, considering possible twisting of the sensor streamer 106, theplane may be defined by the ropes 604 and 606 over a short distancebefore and after the location of the source of vibrations 612. In yetfurther still cases, the source of vibrations may selectively induce theknown vibration in both directions. The specification now turns toexample systems to implement the source of vibrations 612.

FIG. 7 shows, in partial block diagram form, an example source ofvibrations 612. In particular, the source of vibrations 612 of FIG. 7comprises an electric motor 700 that defines a rotatable shaft 702.Coupled to the rotatable shaft is an eccentric weight 704. The eccentricweight has a center of mass that does not correspond to the locationwhere the rotatable shaft 702 couples to the eccentric weight. In thisway, as the electric motor 700 turns the rotatable shaft, the eccentricweight produces mechanical vibrations related to the speed of rotationof the rotatable shaft 702. The electric motor 700 electrically couplesto a motor control circuit 706, and the motor control circuit 706 alsocommunicatively couples to the communication pathway 610 (FIG. 6). Themotor control circuit 706 selectively activates the electric motor 700to create known vibrations for the purpose of creating and/or adjustingthe model of noise propagation along the sensor streamer. The electricmotor 700 may take any suitable form, such as a direct current (DC)motor, an alternating current (AC) motor, a stepper motor, and the like.Correspondingly, the motor control circuit 706 is designed andconstructed to operate the specific type of electric motor 700, based oncommands received over the communication pathway 610 (FIG. 6). In theexample system, power to operate the electric motor 700 and the motorcontrol circuit 706 is drawn from a local battery 708, but in othercases power to operate the various devices may be supplied across thecommunication pathway 610 (FIG. 6).

FIG. 8 shows, in partial block diagram form, another example source ofvibrations 612. In particular, the source of vibrations 612 of FIG. 8comprises a voice coil 800 that includes a winding or solenoid 802 and aplunger 804. When the solenoid 802 is energized, the plunger 804 resides(at least partially) within magnetic flux paths created by the solenoid(the magnetic flux paths not shown so as not to unduly complicate thefigure). In some cases, the solenoid is fixed relative to the outerjacket of the sensor streamer, and the plunger 804 moves within themagnetic flux path (e.g., fixed coil audio speaker). In other cases, theplunger 804 is fixed relative to the outer jacket of the sensorstreamer, and the solenoid 802 moves within the magnetic flux path(e.g., a moving coil audio speaker). Regardless, the relative movementof the plunger 804 and the solenoid 802 produces mechanical vibrationsrelated to the frequency of a driving electrical signal applied to thesolenoid. The voice coil 800 electrically couples to a voice coilcontrol circuit 806, and the voice coil control circuit 806 alsocommunicatively couples to the communication pathway 610 (FIG. 6). Thevoice coil control circuit 806 selectively activates the voice coil 800to create known vibrations for the purpose of creating and/or adjustingthe model of noise propagation along the sensor streamer. In the examplesystem, power to operate the voice coil 800 and the voice coil controlcircuit 806 is drawn from a local battery 808, but in other cases powerto operate the various devices may be supplied across the communicationpathway 610 (FIG. 6).

FIG. 9 shows, in partial block diagram form, another example source ofvibrations 612. In particular, the source of vibrations 612 of FIG. 9comprises a stack of piezoelectric elements 900. Piezoelectric elementshave the property that, when exposed to an electric field, the elementsdeform. When the electric field is removed the elements return to theiroriginal shape. Using this physical phenomenon, known vibrations can becreated by applying an AC electric field to the piezoelectric elements900. The piezoelectric elements 900 electrically couple to apiezoelectric control circuit 902, and the piezoelectric control circuit902 also communicatively couples to the communication pathway 610 (FIG.6). The piezoelectric control circuit 902 selectively activates thepiezoelectric stack 900 to create known vibrations for the purpose ofcreating and/or adjusting the model of noise propagation along thesensor streamer. In the example system, power to operate thepiezoelectric stack 900 and the piezoelectric control circuit 902 isdrawn from a local battery 904, but in other cases power to operate thevarious devices may be supplied across the communication pathway 610(FIG. 6).

The example sources of vibrations 612 of FIGS. 7, 8, and 9 each have asingle vibrational element creating the known vibrations. Theorientation of the single element may define whether the vibrations arecreated perpendicular to the plane defined by the two ropes 604 and 606(FIG. 6, and e.g., in the Z direction of the coordinate system of FIG.6) or parallel to the ropes (e.g., in the X-Y plane of the coordinatesystem of FIG. 6). For example, if the plunger 804 of FIG. 8 oscillateswithin the plane defined by the ropes at the location of the source ofvibrations 612, then the known vibrations will be induced in the plane.Likewise, if the plunger 804 of FIG. 8 oscillates perpendicular to theplane defined by the ropes at the location of the source of vibrations612, then the known vibrations will be induced perpendicular to theplane. Similarly for the piezoelectric stack 900 in relation to thedirection of expansion and contraction based on applied electric fields.The orientation of the vibrations created by the eccentric weight dependon the orientation of the rotatable shaft 702, but also on the directionof the force of gravity (which may change based on twisting of thesensor streamer), but similar ideas apply.

Moreover, if known vibrations are desired both parallel andperpendicular to the plane of the ropes, or selectively induced eitherparallel or perpendicular to the plane, then the vibrational elementswithin each source of vibration can be duplicated. For example,referring to the embodiments of FIG. 8, a first plunger (and associatedsolenoid) can be placed within the plane of the ropes, and a secondplunger (and associated solenoid) can be placed perpendicular to theplane of the ropes, and each solenoid can be selectively activated.

The timing for inducing the known vibrations onto the sensor streamermay likewise take many forms. In some example embodiments the knownvibrations are induced during a period of time after a shot, but beforethe first returns of seismic waves from the seafloor and/or formationsbelow the seafloor. In this way, the model of noise propagation alongthe sensor streamer may be created and/or updated based on the state ofthe sensor streamer just moments before the seismic signals arerecorded. In other cases, the known vibrations are induced during aperiod of time after the last return of waves signal from a first shot,but prior to an immediately subsequent shot. Thus, the model of noisepropagation along the streamer may be created and/or updated based onthe state of the sensor streamer just after the seismic signals arerecorded. It may also be created prior to the commencement of thesurvey.

In yet still other cases, the known vibrations may be induced duringperiods of time when the seismic waves from the shot are impinging onthe sensors of the sensor streamer, and thus the known vibrationsoverlap in time with the seismic signals. In some of these overlapcases, the frequency of the known vibrations may be selected or adjustedto be outside a band of frequencies of interest of the seismic signals.In yet still other cases when the known vibrations are induced duringperiods of time when the seismic waves are impinging on the sensors ofthe sensor streamer, the known vibrations may the form of an encodedsignal which can be separated from the seismic signal (e.g.,spread-spectrum encoded signals like code division multiple access).

In yet still other cases, the inducing of the known vibrations may takeplace in the relation to sail lines. A sail line is a straight path oftravel of the survey vessel in the body of water, the path of travel inrelation to an underground formation of interest. In many cases the pathof travel will be directly above the underground formation of interest,but not in all cases. Regardless, the survey vessel sails along a firstsail line for predetermined distance making many shots and collectingdata for each shot. The survey vessel then makes a 180 degreedirectional turn to sail along a second sail line, where the second sailline is parallel to but offset from the first sail line. Inducing theknown vibrations then may involve inducing at the beginning of a sailline prior to the first shot along the sail line. In other cases,inducing the known vibrations may involve inducing at the end of a sailline after return of seismic waves from the last shot of the sail line.

Returning to FIG. 6, the source of vibrations 612 is a source whoseprimary function is creation of the known vibrations; however, in othercases the source of vibrations may serve a dual purpose. Still referringto FIG. 6, the example sensor streamer 106 also comprises a streamerpositioning device 152. As previously mentioned, the streamerpositioning device 152 may assist in maintaining depth of the sensorstreamer 106, and also lateral positioning of the sensor streamer 106.To accomplish the depth and lateral position control, the streamerpositioning device 152 may comprise a plurality of wings. For streamerpositioning devices that control depth and lateral position, three wingsmay be used, and in the view of FIG. 6 two wings 614 and 616 arevisible, with the third wing hidden by the sensor streamer 106. Thediscussion that follows is equally applicable to streamer positioningdevices that only control depth and have only two wings (such asstreamer positioning devices 150 discussed with respect to FIG. 1).

As alluded to in reference to FIG. 2, streamer positioning devicescreate noise, and thus in further example embodiments the streamerpositioning devices, such as streamer positioning device 152, are usedas a source of vibrations 618 for creating and/or modifying the model ofnoise propagation along the sensor streamer. In particular, the noisecreated by a streamer positioning device is dependent upon the speed ofthe movement of the sensor streamer 106 through the water, and also onthe deflection of the wings (e.g., 614 and 616) to maintain depth andlateral position. A priori, the position of each streamer positioningdevice is known, and thus the noise associated with the streamerpositioning device can be used to create and/or update the model ofnoise propagation.

While in some cases knowing just the locations of the streamerpositioning device provides sufficient information with which to createand/or update the model of noise propagation, in yet still other casesthe nature of the noise (e.g., spectral information, amplitude) may alsobe used for better refinement of the model of noise propagation. Becausethe nature of the noise created by a streamer positioning device changesover time (e.g., as the deflection of the wings takes place), in yetstill further embodiments the noise created by the streamer positioningdevice is measured proximate to the streamer positioning device. In somecases, a dedicated geophone may be placed on or near the streamerpositioning device, such as geophone 620. Thus, given the known locationof the streamer positioning device 152, and the known amplitude andspectral content of the noise as measured by the geophone 620, the modelof the noise propagation may be created and/or updated. In yet stillother cases, rather than using a dedicated geophone, the closestgeophone of a sensor 116 may be used to read the amplitude and spectralcontent of the noise created by the streamer positioning device 152. Inthe example case of FIG. 6, a sensor 622 closest to the streamerpositioning device (and more particularly the geophone of the sensor622) may be used to measure the amplitude and spectral content of thenoise created by the streamer positioning device 152. Of course, in thecase of the streamer positioning device 152 as a source of vibrations618, the primary function of the streamer positioning device 152 ispositioning, with the secondary function being the creation of the knownvibrations with which to create and/or modify the model of noisepropagation along the sensor streamer 106.

FIG. 10 shows, in block diagram form, a method in accordance withexample embodiments, some of which may be performed using a computersystem. In particular, the method starts (block 1000) and comprises:towing a sensor streamer through a body of water, the sensor streamercomprising a plurality of geophones spaced along the sensor streamer(block 1004); inducing a vibration onto the sensor streamer at apredetermined location, the inducing as the sensor streamer is towed(block 1008); measuring the vibration by a geophone at a distance fromthe predetermined location, the measuring creates a measured vibration(block 1012); creating a model of noise propagation along the sensorstreamer, the creating based on the measured vibration (block 1016);creating a data set by reading data from the geophones (block 1020);reducing noise from the data set using the model of noise propagationalong the streamer (block 1024); and recording corrected data to atangible data storage medium (1028). Thereafter, the method ends (block1030).

FIG. 11 shows, in block diagram form, a computer-implemented method inaccordance with example embodiments. In particular, the method starts(block 1100) and comprises: reading a data set containing noise, seismicsignals, and known vibrations recorded by geophones disposed in a sensorstreamer when the sensor streamer was within a body of water (block1104); calculating parameters of a model of noise propagation along thesensor streamer, the parameters calculated using the known vibrations(block 1108); de-propagating noise within the data set using the dataset and the model of noise propagation along the sensor streamer, thede-propagating determines locations of noise sources along the sensorstreamer when the sensor streamer was within the body of water (block1112); suppressing data of the data set corresponding to noise sourcesalong the sensor streamer (block 1116); and recording corrected data toa tangible data storage medium (block 1120). Thereafter, the method ends(block 1124).

FIG. 12 shows a computer system 1200 in accordance with at least someembodiments. The computer system 1200 is an example of: a computersystem upon which portions of the example methods discussed could beperformed; a computer system that forms a part or all of the systemsdescribed; or a computer system that creates the geophysical dataproduct. The example computer system 1200 comprises a processor 1202coupled to a memory 1204 and a storage system or long term storagedevice 1206. The processor 1202 may be any currently available orafter-developed processor, or group of processors. The memory 1204 maybe random access memory (RAM) which forms the working memory for theprocessor 1202. In some cases, data and programs may be copied from thestorage device 1206 to the memory 1204 as part of the operation of thecomputer system 1200.

The long term storage device 1206 is a device or devices that implementnon-volatile long-term storage, which may also be referred to as anon-transitory computer-readable media. In some cases, the long termstorage device is a hard drive or solid state drive, but other examplesinclude optical discs 1208, “floppy” disks 1210, and flash memorydevices 1212. The various programs used to implement the programmaticaspects may thus be stored on the long term storage device 1206, andexecuted by the processor 1202. Relatedly, the noise reduction of thevarious embodiments may be calculated by the processor 1202 andcommunicated to the storage device 1206 (including the example opticaldisc 1208, floppy disk 1210, or flash memory device 1212) by way of atelemetry channel 1214 to become a geophysical data product.

In accordance with a number of embodiments of the present disclosure, ageophysical data product may be produced. The geophysical data productmay include, for example, data where the noise has been de-propagatedand suppressed. Geophysical data, such as data previously collected bysensors, may be obtained (e.g., retrieved from a data library) and maybe stored on a non-transitory, tangible computer-readable medium. Thegeophysical data product may be produced by processing the geophysicaldata offshore (i.e., by equipment on a vessel) or onshore (i.e., at afacility on land). In some instances, once onshore, geophysicalanalysis, including further data processing, may be performed on thegeophysical data product. In some instances, geophysical analysis may beperformed on the geophysical data product offshore. For example, thede-propagation of noise using the model and suppressing data associatedwith noise sources, may be performed on a vessel at sea.

References to “one embodiment”, “an embodiment”, “a particularembodiment”, and “some embodiments” indicate that a particular elementor characteristic is included in at least one embodiment of theinvention. Although the phrases “in one embodiment”, “an embodiment”, “aparticular embodiment”, and “some embodiments” may appear in variousplaces, these do not necessarily refer to the same embodiment.

The above discussion is meant to be illustrative of the principles andvarious embodiments of the present invention. Numerous variations andmodifications will become apparent to those skilled in the art once theabove disclosure is fully appreciated. For example, each sensor streamer106 may comprise multiple individual sections electrically andmechanically coupled end-to-end to form each overall streamer 106. It isintended that the following claims be interpreted to embrace all suchvariations and modifications.

What is claimed is:
 1. A computer-implemented method of processingseismic data to reduce noise, the method comprising: reading, by acomputer system, an original data set recorded by geophones disposedwithin an outer jacket of a sensor streamer when the sensor streamer waswithin a body of water, the original data set containing seismic signalsand noise from actual noise sources outside and coupled to the outerjacket; de-propagating noise within the original data set using theoriginal data set and a model of noise propagation along the sensorstreamer, the de-propagating to determine locations of noise sourcesalong the sensor streamer when the sensor streamer was within the bodyof water, the de-propagating comprising: modelling a plurality of noisesources along the model of noise propagation along the sensor streamer,the modelling creating a model of noise source locations; andidentifying locations of actual noise sources outside the outer jacketand along the sensor streamer by solving the model of noise sourcelocations and the model of noise propagation; suppressing, by thecomputer system, data of the original data set corresponding to actualnoise sources along the sensor streamer; and thereby creating areplacement data set having reduced noise compared to the original dataset.
 2. The method of claim 1 wherein modelling the plurality of noisesources further comprises modelling each noise source as a white noisesource.
 3. The method of claim 1 wherein modelling further comprisesusing the model of noise propagation that defines a plurality ofsegments between geophones, where each segment has a propagation speedas a function of noise frequency and an attenuation as a function ofnoise frequency.
 4. The method of claim 1 further comprising suppressingdata that falls outside a signal cone.
 5. The method of claim 1 whereinde-propagating further comprises determining data indicative ofamplitude of noise sources along the sensor streamer when the sensorstreamer was within the body of water.
 6. The method of claim 1 whereinde-propagating noise within the data set further comprises determininglocations of the noise sources based on amplitude of data within thedata set having frequencies above 100 Hz.
 7. A system comprising: aprocessor; a memory coupled to the processor; and wherein the memorystores a program that, when executed by the processor, causes theprocessor to: read an original data set recorded by geophones disposedwithin an outer jacket of a sensor streamer when the sensor streamer waswithin a body of water, the original data set containing seismic signalsand noise from actual noise sources outside the outer jacket;de-propagate noise within the data set using the original data set and amodel of noise propagation along the sensor streamer by causing theprocessor to: model a plurality of noise sources along the model ofnoise propagation along the sensor streamer, the modelling creates amodel of noise source locations; and identify locations of actual noisesources outside the outer jacket and along the sensor streamer bysolving the model of noise source locations and the model of noisepropagation; suppress data of the original data set corresponding toactual noise sources along the sensor streamer, and thereby creating areplacement data set that has reduced noise compared to the originaldata set.
 8. The system of claim 7 wherein when the processor models theplurality of noise sources, the program causes the processor to modeleach noise source as a white noise source.
 9. The system of claim 7wherein when the processor models a plurality of noise sources, theprogram causes the processor to use the model of noise propagation thatdefines a plurality of segments between geophones, where each segmenthas a propagation speed as a function of noise frequency and anattenuation as a function of noise frequency.
 10. The system of claim 7wherein when the processor suppresses data, the program causes theprocessor to suppress data that falls outside a signal cone.
 11. Thesystem of claim 7 wherein when the processor de-propagates, the programcauses the processor to determine data indicative of amplitude of noisesources along the sensor streamer when the sensor streamer was within abody of water.
 12. The system of claim 7 wherein when the processorde-propagates noise within the data set, the program causes theprocessor to determine locations of the noise sources based on amplitudeof data within the data set having frequencies above 100 Hz.
 13. Amethod of generating a geophysical data product comprising: obtaininggeophysical data recorded by geophones disposed within an outer jacketof a sensor streamer when the sensor streamer was within a body ofwater, the geophysical data containing seismic signals and noise fromactual noise sources disposed outside the outer jacket; modelling aplurality of noise sources along a model of noise propagation along thesensor streamer, the modelling creating a model of noise sourcelocations; identifying locations of actual noise sources along thesensor streamer by solving the model of noise source locations and themodel of noise propagation; suppressing data within the geophysical datacorresponding to actual noise sources along the sensor streamer, therebycreating modified data that has reduced noise compared to thegeophysical data; and recording the modified data in a tangible datastorage medium.
 14. The method of claim 13 wherein modelling furthercomprises using the model of noise propagation that defines a pluralityof segments between geophones, where each segment has a propagationspeed as a function of noise frequency and an attenuation as a functionof noise frequency.
 15. A computer-implemented method of reducing noisein seismic data comprising: reading, by a computer system, an originaldata set containing noise and seismic signals recorded by geophonesdisposed in a sensor streamer when the sensor streamer was within a bodyof water; determining, by the computer system, location of actual noisesources associated with the sensor streamer when the sensor streamer waswithin the body of water by: creating a model of noise propagation alongthe sensor streamer; creating a model of noise sources along the sensorstreamer, the model of noise sources having a plurality of assumed noisesources spaced along the sensor streamer; solving the model of noisepropagation and the model of noise sources to create a model solutionusing the original data set; identifying locations of actual noisesources along the sensor streamer using the model solution; suppressing,by the computer system, data corresponding to the actual noise sourcesalong the sensor streamer; and thereby creating a replacement data sethaving reduced noise compared to the original data set.
 16. Thecomputer-implemented method of claim 15 wherein creating the model ofnoise propagation further comprises creating the model of noisepropagation that defines a plurality of segments between geophones,where each segment has a propagation speed as a function of noisefrequency and an attenuation as a function of noise frequency.
 17. Thecomputer-implemented method of claim 15 wherein identifying locations ofactual noise sources further comprises: identifying assumed noisesources of the plurality of noise sources as actual noise sources if theassumed noise sources have an amplitude above a predetermined thresholdor a spectral content above a predetermined threshold; and refrainingfrom identifying assumed noise sources of the plurality of assumed noisesources as actual noise sources if the assumed noise sources have anamplitude below a predetermined threshold or a spectral content below apredetermined threshold.